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Disease progression model of 4T1 metastatic breast cancer

Journal of Pharmacokinetics and Pharmacodynamics volume 47, pages 105–116 (2020)Cite this article

Abstract

Cancer metastasis is the main cause of death in various types of cancer. However, in the field of pharmacometrics, cancer disease progression models focus on the growth of primary tumors with tumor volume or weight as target values, while the metastasis process is less mentioned. We propose a series of mathematical models to quantitatively describe and predict the disease progression of 4T1 breast cancer in the aspect of primary breast tumor, lung metastasis and white blood cell. The 4T1 cells were injected into breast fat pad of female BALB/c mice to establish an animal model of breast cancer metastasis. The number and volume of lung metastases at different times were measured. Based on the above data, a disease progression model of breast cancer lung metastasis was established and parameter values were estimated. The white blood cell growth and the primary tumor growth of 4T1 mouse are also modeled. The established models can describe the lung metastasis of 4T1 breast cancer in three aspects: (1) the increase in metastasis number; (2) the growth of metastasis volume; (3) metastasis number-size distribution at different time points. Compared with the prior metastasis models based on von Forester equation, our models distinguished the growth rate of primary tumor and metastasis and got parameter values for 4T1 mouse model. And the current models optimized the metastasis number-size distribution model by utilizing logistic function instead of the prior power function. This study provides a comprehensive description of lung metastasis progression for 4T1 breast cancer model, as well as an alternative disease progression model structure for further pharmacodynamics modeling.

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Abbreviations

-2LL:

-2 Times the maximum likelihood logarithm

AIC:

Akaike's information criteria

IIV:

Inter individual variability

GOF:

Goodness of fit

IPRED:

Individual predictions

CWRES:

Conditional weighted residual

References

  1. Chen W, Zheng R, Baade PD, Zhang S, Zeng H, Bray F, Jemal A, Yu XQ, He J (2015) Cancer statistics in China. CA Cancer J Clin 66:115–132. https://doi.org/10.3322/caac.21338

    CAS  Article  Google Scholar 

  2. Peng Z, Wei J, Lu X, Zheng H, Zhong X, Gao W, Chen Y, Jing J (2016) Treatment and survival patterns of Chinese patients diagnosed with breast cancer between 2005 and 2009 in Southwest China. Medicine (Baltimore). https://doi.org/10.1097/MD.0000000000003865

    PubMed  PubMed Central  Article  Google Scholar 

  3. Koch G, Walz A, Lahu G, Schropp J (2009) Modeling of tumor growth and anticancer effects of combination therapy. J Pharmacokinet Pharmacodyn 36:179–197. https://doi.org/10.1007/s10928-009-9117-9

    CAS  PubMed  Article  Google Scholar 

  4. Norton L, Simon R, Brereton HD, Bogden AE (1976) Predicting the course of Gompertzian growth. Nature 264:542. https://doi.org/10.1038/264542a0

    CAS  PubMed  Article  Google Scholar 

  5. Lord BI (1978) Growth kinetics of tumours. Br J Cancer 37:648–649

    PubMed Central  Article  Google Scholar 

  6. Norton L (1988) A gompertzian model of human breast cancer growth. Cancer Res 48:7067–7071

    CAS  PubMed  Google Scholar 

  7. Simeoni M (2004) Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res 64:1094–1101. https://doi.org/10.1158/0008-5472.CAN-03-2524

    CAS  PubMed  Article  Google Scholar 

  8. Ait-Oudhia S, Mager DE (2016) Array of translational systems pharmacodynamic models of anti-cancer drugs. J Pharmacokinet Pharmacodyn 43:549–565. https://doi.org/10.1007/s10928-016-9497-6

    CAS  PubMed  Article  Google Scholar 

  9. Khosravan R, Motzer RJ, Fumagalli E, Rini BI (2016) Population pharmacokinetic/pharmacodynamic modeling of sunitinib by dosing schedule in patients with advanced renal cell carcinoma or gastrointestinal stromal tumor. Clin Pharmacokinet 55:1251–1269. https://doi.org/10.1007/s40262-016-0404-5

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  10. Shigesada N, Kawasaki K, Takeda Y (1996) Modeling stratified diffusion in biological invasions. Oceanogr Lit Rev 2:168–169

    Google Scholar 

  11. Iwata K, Kawasaki K, Shigesada N (2000) A dynamical model for the growth and size distribution of multiple metastatic tumors. J Theor Biol 203:177–186. https://doi.org/10.1006/jtbi.2000.1075

    CAS  PubMed  Article  Google Scholar 

  12. Baratchart E, Benzekry S, Bikfalvi A, Colin T, Cooley LS, Pineau R, Ribot EJ, Saut O, Souleyreau W (2015) Computational modelling of metastasis development in renal cell carcinoma. PLOS Comput Biol 11:e1004626. https://doi.org/10.1371/journal.pcbi.1004626

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  13. Oda T, Miyao N, Takahashi A, Yanase M, Masumori N, Itoh N, Tamakawa M, Tsukamoto T (2001) Growth rates of primary and metastatic lesions of renal cell carcinoma. Int J Urol 8:473–477. https://doi.org/10.1046/j.1442-2042.2001.00353.x

    CAS  PubMed  Article  Google Scholar 

  14. Deryugina EI, Kiosses WB (2017) Intratumoral cancer cell intravasation can occur independent of invasion into the adjacent stroma. Cell Rep 19:601–616. https://doi.org/10.1016/j.celrep.2017.03.064

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  15. Liu Y, Cao X (2016) Characteristics and significance of the pre-metastatic niche. Cancer Cell 30:668–681. https://doi.org/10.1016/j.ccell.2016.09.011

    CAS  PubMed  Article  Google Scholar 

  16. Chin AR, Wang SE (2016) Cancer tills the premetastatic field: mechanistic basis and clinical implications. Clin Cancer Res Off J Am Assoc Cancer Res 22:3725–3733. https://doi.org/10.1158/1078-0432.CCR-16-0028

    CAS  Article  Google Scholar 

  17. Tao K, Fang M, Alroy J, Sahagian GG (2008) Imagable 4T1 model for the study of late stage breast cancer. BMC Cancer 8:228. https://doi.org/10.1186/1471-2407-8-228

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  18. Rashid OM, Nagahashi M, Ramachandran S, Dumur CI, Schaum JC, Yamada A, Aoyagi T, Milstien S, Spiegel S, Takabe K (2013) Is tail vein injection a relevant breast cancer lung metastasis model? J Thorac Dis 5:385–392. https://doi.org/10.3978/j.issn.2072-1439.2013.06.17

    PubMed  PubMed Central  Article  Google Scholar 

  19. Kaur P, Nagaraja GM, Zheng H, Gizachew D, Galukande M, Krishnan S, Asea A (2012) A mouse model for triple-negative breast cancer tumor-initiating cells (TNBC-TICs) exhibits similar aggressive phenotype to the human disease. BMC Cancer 12:120. https://doi.org/10.1186/1471-2407-12-120

    PubMed  PubMed Central  Article  Google Scholar 

  20. Pulaski BA, Ostrand-Rosenberg S (2001) Mouse 4T1 Breast Tumor Model. In: Coligan JE, Bierer BE, Margulies DH, Shevach EM, Strober W (eds) Current protocols in immunology. Wiley, Hoboken

  21. Gao Z-G, Tian L, Hu J, Park I-S, Bae YH (2011) Prevention of metastasis in a 4T1 murine breast cancer model by doxorubicin carried by folate conjugated pH sensitive polymeric micelles. J Controll Release 152:84–89. https://doi.org/10.1016/j.jconrel.2011.01.021

    CAS  Article  Google Scholar 

  22. duPre’ SA, Hunter KW (2007) Murine mammary carcinoma 4T1 induces a leukemoid reaction with splenomegaly: association with tumor-derived growth factors. Exp Mol Pathol 82:12–24. https://doi.org/10.1016/j.yexmp.2006.06.007

    CAS  PubMed  Article  Google Scholar 

  23. Kowanetz M, Wu X, Lee J, Tan M, Hagenbeek T, Qu X, Yu L, Ross J, Korsisaari N, Cao T, Bou-Reslan H, Kallop D, Weimer R, Ludlam MJC, Kaminker JS, Modrusan Z, van Bruggen N, Peale FV, Carano R, Meng YG, Ferrara N (2010) Granulocyte-colony stimulating factor promotes lung metastasis through mobilization of Ly6G+Ly6C+ granulocytes. Proc Natl Acad Sci 107:21248–21255. https://doi.org/10.1073/pnas.1015855107

    PubMed  Article  Google Scholar 

  24. Lin EY, Nguyen AV, Russell RG, Pollard JW (2001) Colony-stimulating factor 1 promotes progression of mammary tumors to malignancy. J Exp Med 193:727–740. https://doi.org/10.1084/jem.193.6.727

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  25. Hölzel D, Eckel R, Emeny RT, Engel J (2010) Distant metastases do not metastasize. Cancer Metastasis Rev 29:737–750. https://doi.org/10.1007/s10555-010-9260-1

    PubMed  Article  Google Scholar 

  26. Tsoularis A, Wallace J (2002) Analysis of logistic growth models. Math Biosci 179:21–55. https://doi.org/10.1016/S0025-5564(02)00096-2

    CAS  PubMed  Article  Google Scholar 

  27. McKendrick AG, Pai MK (1912) XLV. The rate of multiplication of micro-organisms: a mathematical study. Proc R Soc Edinb 31:649–653. https://doi.org/10.1017/S0370164600025426

    CAS  Article  Google Scholar 

  28. Liotta LA, Saidel GM, Kleinerman J (1976) Stochastic model of metastases formation. Biometrics 32:535–550. https://doi.org/10.2307/2529743

    CAS  PubMed  Article  Google Scholar 

  29. Fidler IJ (2003) The pathogenesis of cancer metastasis: the “seed and soil” hypothesis revisited. Nat Rev Cancer 3:453–458. https://doi.org/10.1038/nrc1098

    CAS  PubMed  Article  Google Scholar 

  30. Psaila B, Lyden D (2009) The metastatic niche: adapting the foreign soil. Nat Rev Cancer 9:285–293. https://doi.org/10.1038/nrc2621

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  31. Kaplan RN, Riba RD, Zacharoulis S, Bramley AH, Vincent L, Costa C, MacDonald DD, Jin DK, Shido K, Kerns SA, Zhu Z, Hicklin D, Wu Y, Port JL, Altorki N, Port ER, Ruggero D, Shmelkov SV, Jensen KK, Rafii S, Lyden D (2005) VEGFR1-positive haematopoietic bone marrow progenitors initiate the pre-metastatic niche. Nature 438:820–827. https://doi.org/10.1038/nature04186

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  32. Fazilaty H, Gardaneh M, Bahrami T, Salmaninejad A, Behnam B (2013) Crosstalk between breast cancer stem cells and metastatic niche: emerging molecular metastasis pathway? Tumour Biol J Int Soc Oncodev Biol Med 34:2019–2030. https://doi.org/10.1007/s13277-013-0831-y

    CAS  Article  Google Scholar 

  33. Incardona F, Doroudchi MM, Ismail N, Carreno A, Griner E, Anna Lim M, Reproducibility Project: Cancer Biology (2015) Registered report: interactions between cancer stem cells and their niche govern metastatic colonization. eLife. https://doi.org/10.7554/eLife.06938

    PubMed  PubMed Central  Article  Google Scholar 

  34. Huang Y, Song N, Ding Y, Yuan S, Li X, Cai H, Shi H, Luo Y (2009) Pulmonary vascular destabilization in the premetastatic phase facilitates lung metastasis. Cancer Res 69:7529–7537. https://doi.org/10.1158/0008-5472.CAN-08-4382

    CAS  PubMed  Article  Google Scholar 

  35. Onder TT, Gupta PB, Mani SA, Yang J, Lander ES, Weinberg RA (2008) Loss of E-cadherin promotes metastasis via multiple downstream transcriptional pathways. Cancer Res 68:3645–3654. https://doi.org/10.1158/0008-5472.CAN-07-2938

    CAS  PubMed  Article  Google Scholar 

  36. Mani SA, Guo W, Liao M-J, Eaton ENG, Ayyanan A, Zhou AY, Brooks M, Reinhard F, Zhang CC, Shipitsin M, Campbell LL, Polyak K, Brisken C, Yang J, Weinberg RA (2008) The epithelial-mesenchymal transition generates cells with properties of stem cells. Cell 133:704–715. https://doi.org/10.1016/j.cell.2008.03.027

    CAS  PubMed  PubMed Central  Article  Google Scholar 

  37. Zheng H, Takahashi H, Murai Y, Cui Z, Nomoto K, Niwa H, Tsuneyama K, Takano Y (2006) Expressions of MMP-2, MMP-9 and VEGF are closely linked to growth, invasion, metastasis and angiogenesis of gastric carcinoma. Anticancer Res 26:3579–3583

    CAS  PubMed  Google Scholar 

  38. Luca M, Huang S, Gershenwald JE, Singh RK, Reich R, Bar-Eli M (1997) Expression of interleukin-8 by human melanoma cells up-regulates MMP-2 activity and increases tumor growth and metastasis. Am J Pathol 151:1105

    CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

This work was funded by Natural Science Foundation of Beijing Municipality (Grant No. 7192100).

Author information

Affiliations

  1. Beijing Key Laboratory of Molecular Pharmaceutics and New Drug Delivery System, Department of Pharmaceutics, School of Pharmaceutical Sciences, Peking University, Beijing, 100191, China

    Liang Yang, Ling Yong, Yaoyao Feng, Yu Fu, Daming Kong, Wei Lu & Tian-yan Zhou

  2. School of Pharmacy, University of Otago, Dunedin, 9054, New Zealand

    Xiao Zhu

Authors
  1. Liang Yang
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  2. Ling Yong
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  3. Xiao Zhu
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  4. Yaoyao Feng
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  5. Yu Fu
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  7. Wei Lu
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  8. Tian-yan Zhou
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Contributions

T-yZ, LY designed research; LY, LY, Y-YF performed experiments; LY, LY, XZ, YF, D-mK, WL performed the mathematical model; LY wrote the paper.

Corresponding author

Correspondence to Tian-yan Zhou.

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The authors declare that they have no conflict of interest.

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All applicable international, national, and/or institutional guidelines for the care and use of animals were followed. All procedures performed in studies involving animals were in accordance with the ethical standards of the Institutional Animal Care and Use Committee of Peking University (LA2018272) at which the studies were conducted.

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Yang, L., Yong, L., Zhu, X. et al. Disease progression model of 4T1 metastatic breast cancer. J Pharmacokinet Pharmacodyn 47, 105–116 (2020). https://doi.org/10.1007/s10928-020-09673-5

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  • DOI: https://doi.org/10.1007/s10928-020-09673-5

Keywords

  • Disease progression model
  • 4T1
  • Breast cancer
  • Lung metastasis
  • Mathematical model